# std::piecewise_linear_distribution

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< cpp‎ | numeric‎ | random

Defined in header `<random>` |  |
template< class RealType = double > class piecewise_linear_distribution; |  | (since C++11)

`std::piecewise_linear_distribution` produces random floating-point numbers, which are distributed according to a linear probability density function within each of the several subintervals \(\small{[b_i, b_{i+1})}\)[bi, bi+1). The distribution is such that the probability density at each interval boundary is exactly the predefined value \(\small{p_i}\)pi.

The probability density for any \(\small{ b_i \le x < b_{i+1} }\)bi≤x<bi+1 is \(\small{p_i\frac{b_{i+1}-x}{b_{i+1}-b_i} + p_{i+1}\frac{x-b_i}{b_{i+1}-b_i} }\)pi

bi+1-x
bi+1-bi

+ pi+1

x-bi
bi+1-bi

, where probability densities at interval boundaries \(\small{p_k}\)pk are calculated as \(\small{w_k/S}\)wk/S where \(\small{S}\)S is the sum of all \(\small{\frac{1}{2}(w_k + w_{k+1})(b_{k+1} - b_k)}\)

1
2

(wk+wk+1)(bk+1−bk).

The set of interval boundaries \(\small{b_i}\)bi and the set of weights at boundaries \(\small{w_i}\)wi are the parameters of this distribution.

`std::piecewise_linear_distribution` satisfies all requirements of RandomNumberDistribution.

### Template parameters

RealType | - | The result type generated by the generator. The effect is undefined if this is not one of float, double, or long double.

### Member types

Member type | Definition
`result_type` (C++11) | RealType
`param_type` (C++11) | the type of the parameter set, see RandomNumberDistribution.

### Member functions

(constructor) (C++11) | constructs new distribution (public member function)
reset (C++11) | resets the internal state of the distribution (public member function)
##### Generation
operator() (C++11) | generates the next random number in the distribution (public member function)
##### Characteristics
intervalsdensities (C++11) | returns the distribution parameters (public member function)
param (C++11) | gets or sets the distribution parameter object (public member function)
min (C++11) | returns the minimum potentially generated value (public member function)
max (C++11) | returns the maximum potentially generated value (public member function)

### Non-member functions

operator==operator!= (C++11)(C++11)(removed in C++20) | compares two distribution objects (function)
operator<<operator>> (C++11) | performs stream input and output on pseudo-random number distribution (function template)

### Example

Run this code

    #include <iomanip>
    #include <iostream>
    #include <map>
    #include <random>
    #include <string>

    int main()
    {
        std::random_device rd;
        std::mt19937 gen{rd()};
        // increase the probability from 0 to 5
        // remain flat from 5 to 10
        // decrease from 10 to 15 at the same rate
        std::vector<double> i{0, 5, 10, 15};
        std::vector<double> w{0, 1, 1, 0};
        std::piecewise_linear_distribution<> d{i.begin(), i.end(), w.begin()};

        std::map<int, int> hist;
        for (int n{}; n < 1e4; ++n)
            ++hist[d(gen)];

        for (auto [x, y] : hist)
            std::cout << std::setw(2) << std::setfill('0') << x
                      << ' ' << std::string(y / 100, '*') << '\n';
    }

Possible output:

    00 *
    01 ***
    02 ****
    03 ******
    04 *********
    05 *********
    06 *********
    07 **********
    08 *********
    09 **********
    10 *********
    11 *******
    12 ****
    13 ***
    14 *

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